`(e^(5logx)-e^(4logx))/(e^(3logx)-e^(2logx))`

Explanation

`(e^(5logx)-e^(4logx))/(e^(3logx)-e^(2logx))dx=int(e^(logx^(5))-e^(logx^(4)))/(e^(logx^(3)-e^(logx^(2))))dx`
`" "=int(x^(5)-x^(4))/(x^(3)-x^(2))dx`
`" "(because e^(logx)=x)`
`=int(x^(4)(x-1))/(x^(2)(x-1))dx=intx^(2)dx=(1)/(3)x^(3)+C`